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MsM LECTURE SERIES Computable General Equilibrium (CGE) Modelling for Management Decisions

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Page 1: Maastricht mba cge

MsM LECTURE SERIESComputable General Equilibrium (CGE) Modelling for Management Decisions

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Lecture outline• How can CGE contribute to decision making?• Why general equilibrium?• Why computable general equilibrium?• What does CGE modelling involve? Isn't it difficult?• Tell me more about those data requirements?• How do you solve one of these models?• Aren't these models just black boxes?• OK, what about model validation?• Could you give me that bottom line, again?

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HOW CAN CGE CONTRIBUTE TO DECISION MAKING?

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Is (CGE) modelling useful?

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Part & parcel of a bigger picture

Sub-sector 1

Sub-sector 2

Sub-sector n

Region A Region B Region N

Macro Environment

Rest

of

Worl

d M

acro

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t

e.g

. Exch

an

ge

rate

se.g

. Tr

ad

ing

P

art

ners

Your Company (Manager)

Sector A Sector B Sector N

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(CGE) Modelling for decision support

• All (CGE) models should ultimately be seen as pedagogical devices, their calculations a means to the end of helping managers/decision-makers think through their decisions.

• For this, the (CGE) model used should be:• Transparent: e.g. understand its structure, trace the flow of

expenditures through its equations, etc.;• Easy to tinker with: flexible (yet realistic/real-world and

logical) assumptions; and• It should be clear what is governing its results.

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(CGE) Modelling for decision support

• Companies and customers operate in a dynamic environment….• Need to better understand:

• the implications of changes to the operating environment of customers

• in turn implications to operations and revenue implications for your company

• Identified need for a strategic information framework to:• provide a logical, standardised and consistent approach to

inform key questions• provide context around your customers within the internal

company as well as the broader national/macro context• provide enhanced strategic decision making information.

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(CGE) Modelling for decision support

• Companies and customers operate in a dynamic environment….• The idea is to understand how the economy links together

(to capture feedback effects) and how these inter-linkages contribute to gains and losses (mainly on an aggregated level) in the broader economy.

• Thus, for a manager, CGE can help you to:• understand the broader economy/environment within which

your company operates; and• understand other aspects of your customers’ business

environments (e.g. impact of changes in the international markets and commodity prices, etc.)

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WHY GENERAL EQUILIBRIUM?

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General Equilibrium theory• Economic models fall into two broad genres:

• Macroeconomic models: belong mostly in central banks• They capture the economy's ups and downs, providing a

compass for the folks with their hands on the monetary tiller.• CGE models: largely ignore the vagaries of the business

cycle• They concentrate on the underlying structure of production,

shedding light on the long-term repercussions of such things as…• the Doha trade round• a big tax reform• a global financial crisis (recession)• economic integration• issues of North-South or South-South trade• climate change• or energy and environmental policies.

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General Equilibrium theory• Both kinds of models share a debt to Leon Walras.• Walras was adamant that one could not explain anything in an economy until one had explained everything.

• Each market—for goods, labour and capital—was connected to every other, however remotely.• This interdependence is apparent whenever faster car

sales in Texas result in an increase in grocery shopping in Detroit, the home of America's “big three” carmakers.

• Or when steep prices for oil lead, curiously enough, to lower US interest rates, because the money the Saudi Arabians and the Russians make from crude is spent on US Treasury bonds.

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General Equilibrium theory• This fundamental insight moved one economist to quote the poetry of Francis Thompson:• “Thou canst not stir a flower/Without troubling of a star.”

• Such thinking comes naturally to economists, but escapes many politicians, who blindly uproot flowers, ignorant of the celestial commotion that may ensue.• They slap tariffs on steel imports, for example, to save jobs

in one area, only to find this costs more jobs in the domestic industries that use the metal.

• GE models can help decision-makers think twice about the knock-on effects of their decisions.

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General Equilibrium theory• Wassily Leontief was one of the first to do more than just theorise about this web of interdependence.

• In 1941 he published his book “The Structure of American Economy”.• It contained an input-output model showing the flow of

commodities and services back and forth among America's households, trading partners and 41 national industries.

• In Leontief's blueprint, each industry is represented by an equation.• The inputs to the industry are entered on one side of the

equation, and the industry's output appears on the other.• Since the output of one industry (e.g. steel) serves as an input

for another (construction), one cannot solve any equation without solving them all simultaneously.

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Why general equilibrium?• GE refers to a state where the needs of all participants in an economy are satisfied.• This implies that there exists no excess of demand for, or

supply of, any goods or services traded in this economy.

• GE models provide a comprehensive and detailed description of an economy…• that is based on microeconomic foundations; and• is consistent with key macroeconomic balances and

principles.

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WHY COMPUTABLE GENERAL EQUILIBRIUM?

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Why CGE?• Two reasons why using CGE models makes sense:

• First, while qualitative results are nice, we typically want to know whether a particular change/shock mattered a lot or a little.

• Second, solid microfoundations enhance managers' ability to understand the behaviour of consumers, producers and the government in an economy.

• The aim of CGE modelling is to convert the abstract representation of an economy into realistic, solvable models of actual economies.

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Strengths of CGE approach• Theoretical consistency.

• Comparative statics and counterfactual simulations.

• Accounting consistency.• Closed system with no leak.

• Capture both direct and indirect inter-sectoral, inter-regional, and inter-temporal effects.

• Clear microeconomic structure with links between micro and macro aspect.

• It can provide managers with a base for dialogue.

• Distributional aspects• ‘everything depends on

everything else’• Ability to disaggregate

sectors of interest.• Facility to evaluating second

best situations.• Improving confidence in

simulation results.• Sensitivity analyses: within

and across models.• Ex-post verifications.• Use also focused models.

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• Simplicity of functional forms• Parameterisation and calibration• Equilibrium is a strong assumption• Possibility of multiple equilibria• Confidence intervals cannot easily be derived• Results can often be a black box to non-specialists• Very intensive in terms of time and data• Not strong on analysing monetary phenomena• Micro behaviour limited

Weaknesses of CGE approach

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WHAT DOES CGE MODELLING INVOLVE? ISN'T IT DIFFICULT?

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What does CGE modelling involve?

• A lot of people seem to think that CGE modelling is difficult: nonsense.

• Take a very simple partial equilibrium question:• How will consumption change when prices rise?

• To answer this question, we need four things.• First, some theory, such as a demand curve.• Second, calibration: the original point on this demand

curve.• Third, an estimate of the size of the shock; and• Fourth, the elasticity of demand.

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What does CGE modelling involve?

• These same four elements are all you need to perform a CGE exercise:• The theory can be whatever you want; but Walrasian

theory can be easily summarised…• for every sector, price equals cost; for every commodity,

demand equals supply; for every household, income equals expenditure.

• Calibration involves putting a number on every input, output, consumer demand, trade flow, and factor endowment and all these flows have to be compatible with each other.

• Next is measuring the exogenous shocks.• Finally, picking elasticities of substitution in the production

and utility functions.

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Steps in CGE modelling

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Comparative Static analysis• CGE models are used mainly

for comparative static analysis (SCA).

• This form of analysis involves comparing equilibrium positions as opposed to examining the path that the market follows when moving from the old to the new equilibrium.

• Results of comparative-static CGE’s all refer implicitly to the economy at some future time period.

Employment

0 T

Change

A

years

B

C

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Dynamic modelling• The example can be viewed as

analogous to CSA example with the exception that the path through time is included.

• The advantages of this technique is:• Although, the net effect is still

positive, (higher growth than in the base case) the growth remains negative. This cannot be deduced from the CSA;

• The adjustment that is required is not positive relative to the base case in all the years under review. Another position that cannot be deduced from the CSA.

1996 1997 1998 1999 2000 2001 2002

70

75

80

85

90

95

100

105

Base

Change

Years

Employment

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The concept of equilibrium• An individual market is in equilibrium when the quantity demanded is equal to the quantity supplied.

• But that is static, partial equilibrium analysis.• General equilibrium analysis deals with the inter-relationships between different markets and different sectors in the economy.

• The simplest model of the economy can be represented as the circular flow of economic activity.

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The circular flow model

If there are m commodity markets and n factor markets there will be altogether m+n markets and m+n equilibrium prices to be determined.

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Setting up a model• What are models?• The equations of a model are statements of the functional relationships between economic variables.

• Generally: QD = QD(P) dQ/dP < 0QS = QS(P) dQ/dP > 0QD = QS

• There are two behavioural equations on describing the equilibrium condition for the market.

• Adding constant terms...• Endogenous and exogenous variables…

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A two sector model• Assume:

• Two goods,• Each produced by one of two firms,• Using two factors of production, capital and labour,• And the factor endowments are fixed,• And the factors are owned by one representative

household.

• A general equilibrium model of this economy should specify:• Demand and supply relations.• The equilibrium condition for each market.• A specification of the income constraint of each of the

economic agents in the economy.

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The demand relations• The consumer is assumed to maximise utility subject to a budget constraint.Maximise U = U(C1,C2)

subject to P1C1 + P2C2 = Y

• From the solution it is possible to derive the demand relations: C1 = C1(P1,P2,Y)

C2 = C2(P1,P2,Y)

C1

C2

U3

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The supply relations• The derivation of the supply relations takes place in two steps:• Determining the cost-minimising quantities of the factors

of production required to produce a given level of output.• Determining the profit-maximising level of output.

• Cost-minimising production:• Certain combinations of capital (K) and labour (L) are

required to produce a given level of output.• The relationship between inputs and outputs is given by

the production function Xi = Xi(Ki,Li)

• The cost of production is determined by the price of capital (r) and the price of labour (l).

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The supply relations• Cost-minimising production:

• The least-cost combination of factors is the solution to the cost-minimisation problem:Minimise TCi = rKi + wLi

subject to Xio = Xio(Ki,Li)

• Where TCi represents the total costs of firm i,

• And Xio is the desired level of output.

XioKi

Li

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The supply relations• Profit-maximising output:

• Each firm is assumed to maximise profits – the difference between total revenue and total cost.

• Xio is the profit-maximising level of output determined for firm i by the price at which it sells its product Pi and by the costs of production.

• The general form of the supply functions is described by the equations X1 = X1(P1,w,r)

X2 = X2(P2,w,r)

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Equilibrium• Equilibrium in the product markets:

• The demand relations C1 = C1(P1,P2,Y)

C2 = C2(P1,P2,Y)

• The supply relations X1 = X1(P1,w,r)

X2 = X2(P2,w,r)• The market clearing equations C1 = X1

C2 = X2

• Equilibrium in the factor markets:• The functions that relate the demand for factors by each

firm to the chosen level of output Xi, and the factor prices r and w, are:K1 = K1(X1,w,r) L1 = L1(X1,w,r)

K2 = K2(X2,w,r) L2 = L2(X2,w,r)

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Equilibrium• Equilibrium in the factor markets:

• The functions that relate the demand for factors by each firm to the chosen level of output Xi, and the factor prices r and w, are:K1 = K1(X1,w,r) L1 = L1(X1,w,r)

K2 = K2(X2,w,r) L2 = L2(X2,w,r)

• In the simple model it is assumed that the total quantities of capital and labour are fixed exogenously at K* and L*.

• Thus, the factor market clearing equations take the form:K1 + K2 = K* L1 + L2 = L*

• Finally there are the income equations of the firms and households.

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Equilibrium• The income equations of the firms and households:

• Each firm makes profits equal to the difference between its total revenue from the sale of its products and its expenditure on factor inputs:Π1 = P1X1 – wL1 – rK1 Π2 = P2X2 – wL2 – rK2

• The household supplies the factor services and also receives the profits of the two firms:

Y = w(L1 + L2) + r(K1 + K2) + Π1 + Π2

• Thus, the general equilibrium system is complete with 15 endogenous variables and 2 exogenous variables.

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The need for a numeraire• Example of ‘homogeneity of degree zero’…• In the model it is not possible to determine the absolute price level, but only relative prices.

• To find the equilibrium prices the answer is to set one price equal to one and then solve the system for all other (relative) prices.

• The good with price set equal to unity is known as the numeraire commodity.

• Choosing the numeraire is known as the ‘normalisation’ procedure.

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Walras’ Law• Walras’s Law states that for a given set of prices, the sum of the excess demand over all markets must be equal to zero.

• Thus,• if all markets but one are in equilibrium, • then the last market is in equilibrium as well.

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Complicating it• The basic two-sector model can be solved numerically.

• To the basic structure one can add:• More sectors.• More factors.• More households.• Macro relations.

• The functions were kept general but one has to consider functional forms of for example the demand functions: Cobb-Douglas, LES, CES…

• Parameters have to be estimated…• Choice of exogenous and endogenous variables…

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Closing the model• In the end, CGE models typically have more variables than equations:• Endogenous variables are explained by the model.• Exogenous variables have to be set by the user.

• The closure is about the choice of exogenous variables.

• The choice of closure affects the length of run, T. In the short-run it is assumed that:• T is long enough for price changes to be transmitted throughout

the economy, and for price-induced substitution to take place.• T is not long enough for investment decisions to greatly affect the

useful size of sectoral capital stocks.• This T might be 2 years.

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Closing the model

Private Consumption

InvestmentGovernment Consumption

Real Wage

Capital StocksTech Change

Rate of return on

capital

Trade balance

Employment

GDP= +++

EndogenousExogenous

SHOCK

• Causation in short-run closure

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Closing the model• A possible long-run closure would:

• Let capital stocks adjust to maintain fixed rates of return.• While aggregate employment is fixed and the real wage

adjusts.

• Note:• Many closures might be used for different purposes.• There is no unique natural or correct closure.• There must be at least one exogenous variable measured

in local currency units.• Normally just one price is called the numeraire – often it is

the exchange rate.• Some quantity variables must also be exogenous, such as

primary factor endowments and final aggregate demands.

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Closing the model• The closure leads to three macro “don’t knows”:

• Absolute price level: Numeraire choice determines whether changes in the real exchange rate appear as changes in domestic prices, or as changes in the exchange rate. Real variables unaffected.

• Labour supply: Closure determines whether labour market changes appear as changes in either wage or employment.

• Size and composition of domestic absorption: Either exogenous or else adjusting to accommodate a fixed trade balance. Closure determines how changes in national income appear.

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TELL ME MORE ABOUT THOSE DATA REQUIREMENTS?

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Data requirements• Data requirements for CGE modelling are enormous.

• True, but think of the alternatives.• If you are prepared to calibrate a model, rather than

estimate it econometrically, then all you need is lots of data for one benchmark period: a census year, for example.

• Calibrating theoretical equations to data for one year can be a lot easier than gathering lots of time series data, and estimating structural or reduced form equations.• For example, you avoid the econometric problems

associated with time series data;• not to mention changes in the way statistics were collected

over time.

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Data requirements• The main source of data for a CGE model is a social accounting matrix (SAM).

• Since a SAM represents the circular flow of income in an economy, it is considered to be a natural candidate for a CGE to be based upon.

• A SAM, coupled with a conceptual framework that contains the behavioural and technical relationships among variables within and among sets of accounts, can be used for the evaluation of the economy-wide effects of exogenous changes.• The conceptual framework is supplied in the form of a CGE

model.

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Broad overview of a CGE modelMac

ro E

cono

mic

theo

ry

Micro Econom

ic

theory

Exte

rnal in

form

ati

on

e.g

. ela

stic

itie

s

Behavioural & technical relationships

Prices (e.g. inflation, exchange rate

wage rates etc.)

Marke

t-clearin

g

conditio

ns

Basic

valu

es

to p

rodu

ctio

n co

sts

and

to

purc

hase

rs' p

rices

Demand

Income

Production

structures

Core Input-Output framework

Industry

Pro

du

ct

Social accounting matrix (SAM)

Households

Income by income groups

Employment Supply of labour

Other

Other

Exp

en

dit

ure

GovernmentImportsExports etc.

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HOW DO YOU SOLVE ONE OF THESE MODELS?

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How do you solve CGE models?• A CGE model is just a system of simultaneous equations.

• Specifying those equations is straightforward, at least if you stick to Walrasian (or almost Walrasian) models.

• Now you have to solve them.• Simultaneous non-linear equation solvers like GAMS, GEMPACK and GAUSS can handle any size shocks.

• To solve a model, you just need to specify it, and come up with the numbers.• This leaves the modeller free to focus on data issues, and

economic intuition.

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Two approaches to CGE modelling

Aus./ORANI-style GEMPACK

• Uses percentage change equations

• Has a big, detailed database • Has industry-specific fixed factors

of production • Has a short-run focus (2 years) • Contains many prices • Shows the winners and losers of

economic shocks or policy interventions

• Has more exogenous variables – missing macro relations

• Has a variety of different “closures”

• Uses an input-output database augmented to a SAM

US/GAMS-style

• Uses levels equations• Uses less detailed data • Has mobile capital and labour• Has a medium- to long-run focus

(7-20 years) • Has few prices • Shows the national welfare

implications of economic shocks or policy interventions

• Is a closed model with labour supply, income-expenditure links

• Has one main closure • Uses a SAM database

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AREN'T THESE MODELS JUST BLACK BOXES?

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Aren't these models just black boxes?

• Not if they're constructed and presented properly.• Remember, the (CGE) model used should be:

• Transparent: e.g. understand its structure, trace the flow of expenditures through its behavioural equations, etc.;

• Easy to tinker with: flexible (yet realistic/real-world and logical) assumptions; and

• It should be clear what is governing its results.

• This will ensure that your reasoning and results are clear and concise.

• CGE's are "theory with numbers" – thus strong theoretical underpinning.

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OK, WHAT ABOUT MODEL VALIDATION?

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What about model validation?• Does the model explain anything we observe today or in the recent past (VALIDATION)?

• Clearly finding better and more systematic ways of subjecting your results to sensitivity analysis is a major challenge for CGE modellers.

• Equally important is finding a way to present the results of such analyses concisely.

• One important contribution of CGE modelling can be to bring out clearly the contingent nature of a lot of our knowledge.

• Solidly grounded uncertainty can be preferable to ignorant certainty.

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COULD YOU GIVE ME THAT BOTTOM LINE, AGAIN?

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A final word…• All (CGE) models are ultimately pedagogical devices...

• They can't provide all of the answers, but they do provide a good start…• Managers can understand the broader economic

environment in which they (and their customers) operate;• Management is still in a position to inform decisions based

on broad assumptions;• As key parameters change “fresh” analysis is possible at

much reduced effort and time requirements;• “Scenario” analysis can be conducted to inform

management decisions; and• A logical, standardised and consistent (and repeatable)

approach to inform relevant key questions is provided.

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Q & A